Question

A correlation between two vanables was found using linear regression. The Y vanable was bank balance, the x vanable college tuition. The correlation coefficient was - 078 . What conclusion can be made from these observations?

a. Since the r value is negative, there is not a strong enough correlation to make any conclusions
b. As tuition increases, bank balance decreases
c. Not enough information is provided to make any conclusions
d. As bank balance increases, tution increases

Answer 1

A correlation coefficient of -0.78 between bank balance and college tuition indicates that as college tuition increases, bank balance tends to decrease. This represents a moderate to strong negative correlation between the two variables.

Step-by-step explanation:

The conclusion that can be made from the observations stating that there is a correlation coefficient of -0.78 between the variables of bank balance (Y variable) and college tuition (X variable) using linear regression is option b. As tuition increases, bank balance decreases. This negative correlation indicates that there is a tendency for the bank balance to go down as the college tuition goes up. It is important to note that while this correlation suggests a relationship between the two variables, it does not necessarily imply causation.

The strength of this negative correlation is considered moderate to strong, given that the correlation coefficient is close to -1. It is also essential to remember that correlation coefficients range from -1 to 1, with values closer to -1 indicating a strong negative correlation, whereas values closer to 1 indicate a strong positive correlation.